Simplify 81/16 whole to power -5/4 …

To simplify the expression, let's first work on each part separately: 1. (81/16)^(-5/4): Recall that when a fraction is raised to a negative exponent, the reciprocal of the fraction is used, and the negative exponent becomes positive. (81/16)^(-5/4) = (16/81)^(5/4) Now, take the fourth root of the numerator and the denominator: (16/81)^(5/4) = [(16)^(1/4)]^5 / [(81)^(1/4)]^5 Simplify the exponents: (16)^(1/4) = 2 (81)^(1/4) = 3 Substitute back: (16/81)^(5/4) = 2^5 / 3^5 = 32 / 243 2. (25/9)^(-5/2): Similarly, apply the same rule for a negative exponent: (25/9)^(-5/2) = (9/25)^(5/2) Now, take the square root of the numerator and the denominator: (9/25)^(5/2) = [(9)^(1/2)]^5 / [(25)^(1/2)]^5 Simplify the exponents: (9)^(1/2) = 3 (25)^(1/2) = 5 Substitute back: (9/25)^(5/2) = 3^5 / 5^5 = 243 / 3125 Now, multiply the two simplified expressions: (32 / 243) * (243 / 3125) The common term "243" cancels out, leaving: 32 / 3125 Thus, the simplified result of the expression is 32/3125.